It matters to a number of projects whether monomorphemic lexical items (‘boy’, ‘cat’, ‘give’, ‘break’, etc.) have internal linguistic structure. (Call the theory that they do the Decomposition Hypothesis (DC).) The cognitive science consensus is, overwhelmingly, that DC is true; for example, that there is a level of grammar at which ‘breaktr’ has the structure ‘cause to breakint’ and so forth. We find this consensus surprising since, as far as we can tell, there is practically no evidence to support it. (For example, there is no psychological evidence that you can’t have a word that expresses the concept BREAKTR unless you have the concept CAUSE. But there ought to be if CAUSE is a constituent of BREAKTR) This isn’t, of course, to say that there are no prima facie arguments at all for DC. The best one’s we’ve heard are the Impossible Word Arguments (IWA). That being so we’re very interested in whether IWAs are, in fact, sound.